Economic Analysis of Results

Economic Analysis of Results#

This guide describes the economic interpretation framework built into GreenBubble’s post-processing pipeline (scripts/plots.py). It covers:

  • how the network represents markets via buses and shadow prices,

  • the product topology (collection bus + delivery bus),

  • the Levelised Cost of Production (LCOP) formula and its components,

  • the KKT-based LCOP verification (zero-profit condition),

  • the short-run marginal cost (SRMC) and merit order,

  • the full KKT revenue and annual profit, and

  • how to interpret LCOP versus the shadow price at the collection bus.

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Network topology as a market#

GreenBubble is a linear PyPSA model. Every bus is a commodity market at a specific location and quality level. The KKT multiplier at a bus (n.buses_t.marginal_price) is the shadow price of the energy balance constraint there — the marginal value of one additional unit of that commodity at that time step.

Links are technologies that convert commodities. A multilink with ports bus0 … busN satisfies:

flow at bus_k = p0 × efficiency_k   (k ≥ 1)
flow at bus0  = −p0                  (convention: bus0 always consumes)

Positive efficiency_k → the link produces at bus_k (output or by-product). Negative efficiency_k → the link consumes from bus_k (additional input).

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Product topology#

Every product (bioCH4, H2, Methanol) uses a two-bus structure:

[technology A] ──┐
[technology B] ──┤──► bioCH4 collection ──► bioCH4 delivery ──► demand / store
[technology C] ──┘              ▲
                       is_product_bus = True
bioCH4 collection

The collection bus. All technologies producing bioCH4 inject here directly via bus1 of their multilink. Tagged is_product_bus=True in the network so post-processing can discover it automatically.

bioCH4 delivery

The delivery bus. The exogenous demand load (demand mode) or the price-setting sale link (price mode) is attached here.

  • Demand mode: a zero-cost {product}_collection_to_demand link transfers product to the delivery bus, where a Load sets the time profile and an optional cyclic Store provides intra-period flexibility.

  • Price mode: a {product}_collection_to_delivery link carries a time-varying marginal_cost equal to the exogenous selling price series. A non-cyclic annual Store (e_nom_max = total_demand) caps cumulative annual production.

The shadow price at the collection bus (λ_collection) is determined at equilibrium by the marginal producer — the highest-cost technology that is still dispatched. Technologies with lower cost earn an intra-marginal rent.

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Shared components#

Compressors, HP storage, and other auxiliary equipment often serve multiple technologies and are modelled as a single shared component (separate carrier). They are not included in the LCOP computation for the production technologies themselves.

Their capital and operational costs appear implicitly via the shadow price at the buses they connect to (e.g. H2 distribution, CO2 distribution). When a production technology draws H2 from H2 distribution, the KKT λ_{H2 distribution} already reflects the full cost of H2 at that pressure level, including compression.

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LCOP — Levelised Cost of Production#

For a multilink lk whose bus1 is a collection bus (is_product_bus=True), first define the indirect OPEX:

\[\text{indirect OPEX} = -\sum_{k \neq 1} \eta_k \cdot \overline{(\lambda_{k} \cdot p_0)}\]

where \(\eta_0 = -1\) for bus0 (primary feedstock, always consumed), and \(\overline{(\lambda_k \cdot p_0)} = \sum_t p_{0,t} \cdot \lambda_{k,t} \cdot w_t\) with snapshot weights \(w_t\) from snapshot_weightings["objective"].

The sign convention makes indirect OPEX positive when input costs dominate (the typical case) and negative only if by-product credits exceed all feedstock costs.

Port contributions to indirect OPEX#

Port

\(\eta_k\)

Contribution to indirect OPEX

bus0 — primary feedstock

−1

\(+p_0 \cdot \lambda_{\text{bus0}} \cdot w\) — adds feedstock cost

bus2..N — additional input

< 0

\(+|\eta_k| \cdot p_0 \cdot \lambda_k \cdot w\) — adds feedstock cost

bus2..N — by-product output

> 0

\(-\eta_k \cdot p_0 \cdot \lambda_k \cdot w\) — subtracts by-product credit

Then:

\[\text{LCOP} = \frac{\text{CAPEX} + \text{OPEX} + \text{indirect OPEX}}{Q_\text{main}}\]

where:

  • \(\text{CAPEX}\) = n.statistics.capex() for the link (annualised capital cost)

  • \(\text{OPEX}\) = n.statistics.opex() for the link (explicit marginal_cost × dispatch — variable O&M such as enzyme or maintenance rates, not feedstock costs)

  • \(Q_\text{main} = \sum_t p_{0,t} \cdot \eta_1 \cdot w_t\) — annual production at bus1

No double-counting: OPEX is the explicit variable O&M declared in tech_costs (VOM). Indirect OPEX captures the market value of feedstocks consumed and by-products produced via KKT shadow prices. These measure different things and do not overlap.

Existing (EXI_) assets: whether CAPEX appears in the LCOP depends on remaining_investment_fraction (rif) in n_config.yaml:

  • rif = 0 (default — sunk cost): capital_cost = 0 in the network, so CAPEX = 0 from statistics. LCOP reflects short-run cost only (OPEX + indirect OPEX).

  • rif > 0 (residual obligation outstanding): capital_cost = rif × I(construction_year) × annuity(amortization_period, discount_rate). CAPEX is non-zero and the LCOP includes this residual capital charge.

See Brownfield initial conditions for the full parameter description.

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Revenue, net market value, and annual profit#

\[\text{revenue main product} = \eta_1 \cdot \sum_t p_{0,t} \cdot \lambda_{\text{bus1},t} \cdot w_t\]

This is the market value of the main product at the collection bus — what the market would pay for everything the technology produces there.

\[\text{net market value} = \text{revenue main product} - \text{indirect OPEX}\]
\[\text{annual profit} = \text{net market value} - \text{CAPEX} - \text{OPEX} = \text{revenue main product} - \text{indirect OPEX} - \text{CAPEX} - \text{OPEX}\]

Annual profit is the economic rent: what the market pays the technology for its product, minus every cost it incurs (capital, O&M, feedstocks net of by-products).

  • annual profit ≈ 0 — the technology is the marginal (price-setting) producer.

  • annual profit > 0 — intra-marginal rent; technology has lower cost than the price-setter.

  • annual profit < 0 — technology is loss-making under current market conditions (possible for EXI_ assets if market prices are low).

Note

The zero-profit condition holds for optimally expanded technologies in a fully endogenous problem. When exogenous selling prices are set (price mode), the complementary slackness argument breaks down and all dispatched technologies can earn positive profit if the price exceeds the LCOP of the marginal producer.

Intra-marginal rent:

rent_per_MWh ≈ λ̄_collection − LCOP

where λ̄_collection is the energy-weighted mean shadow price at the collection bus (from shadow_prices_mean.csv). The technology with LCOP ≈ λ̄_collection is the price-setter; all others earn rent proportional to the cost gap.

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Output files#

The following output files are generated by scripts/plots.py:

csv/lcop_by_technology.csv

One row per product link (index column: link).

Column

Description

carrier

PyPSA carrier name of the link

product

Product name (bioCH4, H2, Methanol …)

CAPEX (EUR)

Annualised capital cost from n.statistics.capex()

OPEX (EUR)

Variable O&M from n.statistics.opex() (explicit marginal cost × dispatch)

indirect OPEX (EUR)

Feedstock costs minus by-product credits via KKT shadow prices; positive = net cost (typical), negative = by-products exceed feedstock cost

revenue main product (EUR)

Market value of annual main-product output at the collection bus

net market value (EUR)

revenue main product − indirect OPEX

annual production (MWh)

Annual energy output at bus1 = \(\sum_t p_{0,t} \cdot \eta_1 \cdot w_t\)

LCOP (EUR/MWh)

(CAPEX + OPEX + indirect OPEX) / annual production

annual profit (EUR)

net market value − CAPEX − OPEX; economic rent earned by the technology
plots/lcop_by_technology.png

Two-panel bar chart: LCOP [€/MWh] (top) and annual profit [k€] (bottom).

csv/lcop_kkt_by_technology.csv

Verification table produced by compute_lcop_kkt_by_technology(). For each product link, LCOP is independently computed as the production-weighted average KKT shadow price at the collection bus:

\[\text{LCOP}_\text{kkt} = \frac{\displaystyle\sum_t w_t \cdot \eta_1 \cdot p_{0,t} \cdot \lambda_{\text{bus1},t}} {\displaystyle\sum_t w_t \cdot \eta_1 \cdot p_{0,t}}\]

At optimum this equals the cost-based LCOP (zero-profit condition). The diff cost−kkt column confirms agreement to < 0.01 €/MWh. Columns: carrier, product, annual_production_MWh, LCOP_cost (EUR/MWh), LCOP_kkt (EUR/MWh), diff cost−kkt (EUR/MWh), π_bus1_mean, π_bus1_std, π_bus1_prod_weighted.

csv/srmc_by_technology.csv / plots/srmc_by_technology.png

Short-run marginal cost (SRMC) computed by compute_srmc_by_technology(). For each product technology at every snapshot:

\[\text{SRMC}_{s,t} = \frac{\lambda_{\text{bus0},t} - \displaystyle\sum_{k \geq 2} \eta_k \cdot \lambda_{\text{bus}_k,t} + \text{VOM}_{s}}{\eta_1}\]

This is the instantaneous cost of producing one more MWh of main product at time t, given current input market prices. It is distinct from the model input marginal_cost on links (which is the VOM, one term in the formula).

The long-form CSV has columns: snapshot, link, product, SRMC_EUR_per_MWh, dispatch_MW, π_product_bus, in_merit (whether SRMC ≤ product shadow price at that hour).

The plot shows one subplot per product with SRMC time series per technology and the product bus shadow price as a dashed reference line.

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Shadow price outputs#

csv/shadow_prices_mean.csv

Energy-weighted mean KKT for every bus in plots_config.yaml → bus_list_mp, including collection buses. Computed regardless of whether any technology actively dispatches to the bus.

Formula:

\[\bar{\lambda}_\text{bus} = \frac{\sum_t \lambda_{t} \cdot q_t \cdot w_t}{\sum_t q_t \cdot w_t}\]

where \(q_t\) is the net injection at the bus (generators + positive-efficiency link outputs + storage discharge), and \(w_t\) is the snapshot weight. Falls back to duration-weighted mean when a bus has no measurable injection.

Columns:

Column

Description

bus (index)

Bus name from bus_list_mp

energy weighted mean (EUR/MWh)

Energy-weighted mean shadow price at that bus
plots/shd_prices_mean_bar.png

Bar chart of energy-weighted mean shadow prices. Collection buses are excluded — delivery buses are sufficient to read the product market price. Buses with no active injection are also dropped.

plots/shd_prices_violin.png, plots/shd_prices_ldc.png

Snapshot distribution of shadow prices (one observation per time step), with the scenario-weighted mean marked. These show when prices are high or low, not an energy-weighted average. Restricted to the same delivery-bus subset as the bar chart, further filtered to buses with at least one injecting link above the LINK_TH capacity threshold.

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Comparing LCOP to shadow prices#

A practical diagnostic workflow:

  1. Look at shadow_prices_mean.csv — read the energy weighted mean (EUR/MWh) for the delivery bus of each product (e.g. bioCH4 delivery) — this is λ̄_delivery, which equals λ̄_collection when the collection-to-delivery link is zero-cost.

  2. Look at lcop_by_technology.csv — compare each technology’s LCOP (EUR/MWh) to λ̄_delivery of its product.

  3. Technologies with annual_profit_EUR ≈ 0 are price-setters.

  4. Technologies with annual_profit_EUR > 0 earn intra-marginal rent — check whether they are EXI_ (legacy) assets or optimally expanded.

  5. In price mode, all technologies that run may earn positive profit if the exogenous selling price exceeds the LCOP of the marginal producer.

  6. Use srmc_by_technology.csv to see when each technology is in-merit (in_merit = True). Hours with SRMC near the shadow price reveal the marginal technology. Large SRMC variance indicates strong sensitivity to electricity or H2 price fluctuations.